This is a blog to discuss philosophy, chess, politics,
C. S. Lewis, or whatever it is that I'm in the mood to discuss.

Saturday, October 08, 2016

Do you accept the law of noncontradiction? Based on what evidence?

Is the law of noncontradiction based on evidence? What possible evidence is there for it or against if? If you accept the law, and it is not based on evidence, does that mean that you accept something without evidence?

22 comments:

The Law of Noncontradiction holds true only for inanimate matter. Amongst us human beings, however.. life is full of contradiction. Just the other day, I saw a car with two bumper stickers on it. The first was one of those "Coexist" stickers made up of various religious symbols - the other was a Trump for President sticker.

The law of non-contradiction is a law of being, so it holds for all beings, whether animate or inanimate.

"Amongst us human beings, however.. life is full of contradiction."

This is a different claim. It is the rather uncontroversial claim, backed by the overwhelming empirical evidence constituted by the entire history of the human race, that no human being (with one exception) is completely consistent in his beliefs.

law of contradistinction is a law about logical contradict ,life being full of contradistinctions are not logical ones because logical contradictions are are impossible., they are a different matter, values sensibility and expectation,

I expect money to come, it does not come, that's a contradiction to my expectation but it'snot a violation of logic,.

"Aristotle himself described his subject matter in a variety of ways: as ‘first philosophy’, or ‘the study of being qua being’, or ‘wisdom’, or ‘theology’"

http://plato.stanford.edu/entries/aristotle-metaphysics/

Simplistically put, Aristotle thought that things behaved the way that they behaved because it was inherent in their nature. A thing was a certain kind of thing because each thing has an essence. Understand the essence of a thing and you understand how that thing behaves. Essences can be grouped into a hierarchy of categories with Being as the highest category. The rules of logic describe how to work with the categories and members of those categories.

"Simplistically put, Aristotle thought that things behaved the way that they behaved because it was inherent in their nature. A thing was a certain kind of thing because each thing has an essence. Understand the essence of a thing and you understand how that thing behaves. Essences can be grouped into a hierarchy of categories with Being as the highest category. The rules of logic describe how to work with the categories and members of those categories."

While this is not fundamentally incorrect (*) as a characterization of what Aristotle holds (or what I hold for that matter), it is misleading in the sense that it goes *way beyond* what I said. Essentialism, and the Aristotelian version of it, is a much stronger claim than the very mild, tame claim that the law of non-contradiction is a law of being. Which claim can be paraphrased in several different ways, say the LNC is about ontology not epistemology.

(*) Being is not an essence so it does not stand at the top of the Porphyrian tree.

In order for the law of noncontradiction to be based on evidence, there has to be a possible set of observations that would disconfirm it. If disconfirmatory evidence is not possible, then there can be no confirmatory evidence.

The LNC does not hold in the Three-value logic, or in Fuzzy Logic, and it is violated inside Quantum Mechanics. So, it is not really a question of 'evidence' to decide if you accept the LNC but which game are we playing.

In Quantum Mechanics, the values of F(a) and not-F(a) are probabilistic. So and electron can be both inside a box and not-inside the box at the same time and in the same sense.

Also, the truth value of (A or B) may depend on the order that the two propostions are confirmed. Not only are the laws of quantum physics different than classical physics but the very foundations of logic are different. *

Paraphrased from _Quantum Mechanics: the Theoretical Minimum_ by Leonard Susskind

"So and electron can be both inside a box and not-inside the box at the same time and in the same sense."

This is false. First if it it were true, it would mean that QM proved an inconsistency, and since by the principle of explosion a consistency entails everything, it would follow that QM proved everything and had no predictive power. Second, as a corollary of the previous and contrary to what you say, the proposition "electron can be both inside a box and not-inside the box at the same time and in the same sense" is *provably* false. The proof is not difficult but it does require that one actually knows QM.

You said you paraphrased; if Sussking actually said that, he is wrong, because QM says no such thing neither it implies such thing. At this point it would be helpful to remind that in the history of QM its founders like Nield Bohr or Heisenber were absolutely adamant on logical consistency -- it is simply a matter of reading their papers. Bohr is especially useful in this regard.

I can even say that I know with almost certainty where the mistake is being made.

QM has a consistent logic, it just isn't the same as classical logic. Think of the rules of logic like the rules of a games. Change the rules and you change the game. Change the rules badly and you get a bad game; change the rules correctly and you get a good (but different) game. Classical logic applies very well in our every day world (except for vague and ambiguous attributes) but it doesn't apply to the realm of QM.

"But the LNC still doesn't hold in a many-valued logic. It is simply not an axiom in those systems."

This is either false or vacuous.

In classical propositional logic, the LNC has a semantic counterpart in that the valuation of a wff has a single value. If we take that as the counterpart of the LNC of other logics then of course it is an axiom of any logic deserving the name, for otherwise it would have no well-defined semantics. The point here is that to be able to affirm that many-valued logics violate (your word, not mine) the LNC without falling into equivocation, one has to establish exactly what is the appropriate LNC-equivalent in said logics. To vary the example, it is rigorously vacuous to say that constructive logic violates the law of excluded middle; constructivists interpret the logical connectives and quantifiers differently than classical logicians so they are not even talking about the same thing.

More importantly even, if one views the LNC as a law of being as I do, and not a formal axiom in some formalized logic, it is irrelevant whether many valued logics violate LNC or not. Such would-be facts only invite a shrug of shoulders.

"Classical logic applies very well in our every day world (except for vague and ambiguous attributes) but it doesn't apply to the realm of QM."

Once again this is simply false; but you are excused because quite obviously you do not know QM.

QM is formulated in classical logic with no problem at all -- that is how all textbooks do it. You must live in Cuckoo land if you think physicists give a rat's ass about such logical niceties. Quantum Logic, which I guess is what you have in mind, and which does exist as a mathematical subject, hardly qualifies as a logic (for various technical reasons I will not go into) and at any rate has gone exactly nowhere as far as physics is concerned and, barring some spectacular new insight, does not seem it ever will. And the same comments as given above apply.

The rest about "consistency" and "rules" and "games" and whatnot is pure irrelevant waffle. But once again, and for the same reason, quite understandable.

Followers

About Me

I am the author of C. S. Lewis's Dangerous Idea: In Defense of the Argument from Reason, published by Inter-Varsity Press. I received a Ph.D in philosophy from the University of Illinois at Urbana-Champaign in 1989.